# A test has a mean of 153 and a standard deviation of 12, how do you find the test scores that correspond to (a) z= 1.2 and (b) z = -2.4?

##### 1 Answer
Jun 23, 2015

The corresponding scores will be (a) 167.4 and (b) 124.2. Assuming we round to the nearest whole number, this would be 167 and 124 respectively.

#### Explanation:

Recall that the Z-score of a data point indicates the number of standard deviations that data point is above or below the mean. Thus, a Z-score of 1.2 on data point (a) indicates that (a) is approximately 1.2 standard deviations above the mean of 153, while data point (b) - possessing a Z-score of -2.4 - would lie 2.4 standard deviations below 153.

Thus, the score for (a) is $a = 153 + 1.2 \left(12\right) = 167.4$, and the score for (b) is $b = 153 - 2.4 \left(12\right) = 124.2$.

Assuming that the test scores must be whole numbers (and thus one cannot gain 0.4 points on a question, for example), we would round these to the nearest whole number, yielding $a = 167 , b = 124$.